A comparative social network analysis of wasp colonies and classrooms: Linking network structure to functioning

A major question in current network science is how to understand the relationship between structure and functioning of real networks. Here we present a comparative network analysis of 48 wasp and 36 human social networks. We have compared the centralisation and small world character of these interaction networks and have studied how these properties change over time. We compared the interaction networks of (1) two congeneric wasp species (Ropalidia marginata and Ropalidia cyathiformis), (2) the queen-right (with the queen) and queen-less (without the queen) networks of wasps, (3) the four network types obtained by combining (1) and (2) above, and (4) wasp networks with the social networks of children in 36 classrooms. We have found perfect (100%) centralisation in a queen-less wasp colony and nearly perfect centralisation in several other queen-less wasp colonies. Note that the perfectly centralised interaction network is quite unique in the literature of real-world networks. Differences between the interaction networks of the two wasp species are smaller than differences between the networks describing their different colony conditions. Also, the differences between different colony conditions are larger than the differences between wasp and children networks. For example, the structure of queen-right R. marginata colonies is more similar to children social networks than to that of their queen-less colonies. We conclude that network architecture depends more on the functioning of the particular community than on taxonomic differences (either between two wasp species or between wasps and humans).

A Shapley Value-Based Approach to Discover Influential Nodes in Social Networks

Our study concerns an important current problem, that of diffusion of information in social networks. This problem has received significant attention from the Internet research community in the recent times, driven by many potential applications such as viral marketing and sales promotions. In this paper, we focus on the target set selection problem, which involves discovering a small subset of influential players in a given social network, to perform a certain task of information diffusion. The target set selection problem manifests in two forms: 1) top-k nodes problem and 2) lambda-coverage problem. In the top-k nodes problem, we are required to find a set of k key nodes that would maximize the number of nodes being influenced in the network. The lambda-coverage problem is concerned with finding a set of k key nodes having minimal size that can influence a given percentage lambda of the nodes in the entire network. We propose a new way of solving these problems using the concept of Shapley value which is a well known solution concept in cooperative game theory. Our approach leads to algorithms which we call the ShaPley value-based Influential Nodes (SPINs) algorithms for solving the top-k nodes problem and the lambda-coverage problem. We compare the performance of the proposed SPIN algorithms with well known algorithms in the literature. Through extensive experimentation on four synthetically generated random graphs and six real-world data sets (Celegans, Jazz, NIPS coauthorship data set, Netscience data set, High-Energy Physics data set, and Political Books data set), we show that the proposed SPIN approach is more powerful and computationally efficient. Note to Practitioners-In recent times, social networks have received a high level of attention due to their proven ability in improving the performance of web search, recommendations in collaborative filtering systems, spreading a technology in the market using viral marketing techniques, etc. It is well known that the interpersonal relationships (or ties or links) between individuals cause change or improvement in the social system because the decisions made by individuals are influenced heavily by the behavior of their neighbors. An interesting and key problem in social networks is to discover the most influential nodes in the social network which can influence other nodes in the social network in a strong and deep way. This problem is called the target set selection problem and has two variants: 1) the top-k nodes problem, where we are required to identify a set of k influential nodes that maximize the number of nodes being influenced in the network and 2) the lambda-coverage problem which involves finding a set of influential nodes having minimum size that can influence a given percentage lambda of the nodes in the entire network. There are many existing algorithms in the literature for solving these problems. In this paper, we propose a new algorithm which is based on a novel interpretation of information diffusion in a social network as a cooperative game. Using this analogy, we develop an algorithm based on the Shapley value of the underlying cooperative game. The proposed algorithm outperforms the existing algorithms in terms of generality or computational complexity or both. Our results are validated through extensive experimentation on both synthetically generated and real-world data sets.